They use different mirror shapes -- the 0-360 version is similar to your drawing, while the EGG is more like what would be left after a circle is swept out of a cylinder, so the effect (as a flat picture) would be different. The EGG is the only current one I could find that didn't have the mirror exposed and at the end of a long, delicate-looking stalk, but since I'm not looking for such a lens myself, I didn't spend a lot of time searching.

(When I wanted a 360° panorama in the film days, I rented a slit-shutter revolving camera. It opened the shutter and rotated the camera through a full circle while advancing the film -- sort of like a flatbed scanner for the world.)